2.8 Power Tips: Simply estimate load transient response

Hi. I'm Robert Kollman. I'm a Senior Applications Manager at Texas Instruments. Welcome to Power Tips. Welcome to Power Tip 10. We're going to talk about how you can simply estimate the low transient response of your power supply. The low transient response to your power supply is set by the output impedance of the power supply.
High output impedance means that you have poor low transient response. Low output impedance means that it has very good transient response. And the close loop output impedance of the power supply is set by the open loop output impedance of the power supply divided by 1 plus loop gain. Now, the loop gain is the function of frequency.
At very low frequency, you usually have lots of gain. And so your regulation is going to be very good. At high frequency, your loop gain has fallen below 1. And your output impedance is simply your open loop output impedance.
We're going to take a look at a couple power stages. This particular one is voltage mode control. This is typically what you'd see in a bucked regulator. We have a voltage controlled voltage source, which represents the PWM switches. We have the output filter inductor along with this equivalent series resistance.
We have the output filter capacitor along with its parasitic components to the ESR and then also the ESL or the capacitor. And then over here on the right, we're shown a driving current. And this current will help us to measure the output impedance. We'll inject a 1 amp current into the output of the power supply here and measure the voltage at this node.
And basically, that's going to be the output impedance at that particular frequency. So over here on the right, we have the frequency characteristics of the power supply. At low frequency, the output impedance is set mainly by the ESR of the output filter inductor. And then as the frequency increases, you start to see the effects of the reactants of the output filter reductor.
And the impedance comes up. At higher frequencies, you see the impact of the output filter capacitor shunning that inductance. And you see the impedance go down.
In between these two points, you see the filter resonance also. And it has a pretty significant peak because these are the low loss elements in the circuit and the Q is very high. As we continue increasing the frequency of the injected signal, you'll see that we actually hit a bottom here. And that's going to be established by the ESR and output filter capacitor. And then the output impedance starts to increase due to the ESL of the output filter capacitor.
This second output impedance that we're going to talk about is current mode controlled. And in this case, we have basically turned the output filter inductor of the power supply into a current source. And it drives the output filter capacitor along with its parasitics. And as you sweep the impedance of this type of control scheme, it seems quite different than the voltage mode.
Rather than having low impedance at low frequency, we had the output impedance of the current source. And that's basically an open circuit. So all this curve is is the output impedance of the output filter capacitor. It starts off capacitive, runs into the ESR minimum here, and then turns inductive at higher frequencies.
Now we're going to combine some of these curves and then calculate what the output impedance of the closed loop is. This first curve here is our open loop output impedance. So you can see the big peak in it from the filter resonance. Here is our overall loop gain.
And again, you can see that we have an integrator type response at low frequency. You can see the impact of our output filter going resonant actually in the gain curve. And then at higher frequencies, we crossover 0 DPU, or that's a gain of 1, and then continue on down.
And so this last curve, this is the output impedance of the power supply versus frequency. We've taken our output impedance, divided it by the loop gain, and this is the result. So you can see, like we discussed earlier, at low frequency, we have very low output impedance because we're starting with a low number and then dividing by lots of gain. And so very low output impedance.
You see as we increase in frequency, the output impedance comes up because we're losing loop gain. And then you see right here as the power supply crosses 0 DB or a gain of 1, that the two curves are about the same. And then at higher frequencies, the gain and the power supply is so little that it has no impact on the output filter impedance. And so at higher frequencies, the output filter impedance follows the open loop output filter.
So we can use these curves to estimate what the power supply transient response is going to be. Basically, the peak power supply output impedance occurs at crossover frequency of the power supply. So simply, we can take the change in output current times this peak output impedance to estimate our transient response. There are a couple caveats that go along with this. If this is a very slowly changing current transition, it'll actually be much better response than what you'll calculate this way.
And then the other thing is that you have to watch out for the ESL of that output filter capacitor because the loop gain is not going to do you any good at very high frequencies. And so that may actually set the transient response if you have some very high slew rates impacting your output filter. The other thing that occurs in power supplies is that you get some peaking depending on your phase margin. And so if you go and calculate what your output impedance is at close loop, you'll see again it's our output impedance open loop.
And now I've shown it divided by 1. And this is the real and imaginary part of the loop gain. And so we have a magnitude of 1. And depends on the relative amplitudes of these two different terms.
If you had cosine equal to 1, you would have 1 minus 1. This would be 0 over here. And you'd have division by 0 or you'd have a very high peak in the output impedance. So you see as you increase the phase margins and get it down to something that's acceptable, like 45 or 60 degrees of phase margin, that should have very little impact on the peaking of the output filter.
Now on this chart, what I have done is I have plotted the closed loop output impedance of a voltage mode and a current mode power supply. Now, the current mode power supply typically is going to have better phase margin, that is because you don't have the complex poles that you do in a voltage mode control. And so you are working basically with a first order system.
And it's pretty easy to get 90 degrees of phase margin and get no peaking at all. With the voltage mode, you're going to have higher peaking. And so your output impedance is typically going to be higher than the current mode control. But the other thing to look at here is if you look at the lower frequencies, you'll see that you have much lower output impedance in the voltage mode control as opposed to the current mode control.
And so this curve compares a transient response of the voltage mode and a current mode power supply. You can see that the amplitude on the output voltage excursion on the current mode is less because it had lower peaks than we saw in the previous chart. But it takes longer to recover than the voltage mode power supply. And that's because the voltage mode power supply has much lower output impedance at the lower frequencies. And so it's able to recover much quicker.
Well, thank you for your attention on this Power Tip. For more Power Tips, visit the Power Management DesignLine and search for Power Tips. It's also at the double E's Times website. Or you can click on the link to All Articles in the description section this video. Thanks.